Brane world cosmology Lecture from the course Introduction
Brane world cosmology Lecture from the course “Introduction to Cosmoparticle Physics” 1
1. Different approaches of investigation Fundamentally theoretic approach. Phenomenological approach. D=4+d superstring U supergravity M-theory (? ) D=10 D 11 Studying possible manifestations of extra dimensions and possibilities of solutions of basic problems facing the M-theory (hierarchy of electroweak and Planck scales: 200 Ge. V 1019 Ge. V, and others) by the example of simple (maybe inconsistent with fundamental theory) models. 2
2. Progress of phenomenological approach 1) Kaluza-Klein type models. Solution of Klein-Gordon equation in 5 dimensions (4 ordinary (x , = 0, … 3) + 1 cylindrical (z)) for massless field gives Whence we have From point of view 4 d space-time a particle has got mass states – “KK-states” Modern experiment restricts extra dimension manifestation so as 1/R > a few 100 Ge. V => R < 10 17 cm. 3
2. Progress of phenomenological approach 2) Capture of the fields by 4 d manifold (brane) Let us take a scalar field ( ) in 5 (infinite) dimensions with potential as shown. It leads to domain wall dividing 5 d space-time on two parts with respect to one (z) of the dimensions. Let a fermion ( ) has a Yukava coupling with given scalar field (h ). Then fermion gets mass states as shown on the picture, where zero-state turns to be localized (“captured”) near z=0 (domain wall), damping as exp(-hv|z|). (products leave 4 d space-time) 4 Capture of gauge fields is more problematic.
2. Progress of phenomenological approach 3) ADD type models (or low energetic gravity). ADD – Arkani-Hamed, Dimopoulos, Dvali Effect of gravitation of brane in 4+d space-time is not taken into account. brane compact with the size R (can be not small) Ordinary matter is considered to be captured on 4 d brane (M 4) of <<R width. Gravity, contrary to ordinary matter, propagates over all D=4+d space-time (M 4 x. Kd – “bulk”). In this case the law of gravity has the form For MPl~1 Te. V we have d=1 is excluded, while d 2 is allowed. Effective 4 d Planck mass (m. Pl) can be much larger than true “bulk” Planck mass (MPl) and the last one can be as small as electroweak scale (~1 Te. V) provided large enough R. That is hierarchy problem of particle physics is reformulated in terms of large extra dimensions. 5
2. Progress of phenomenological approach 3) ADD type models (or low energetic gravity). At E~MPl there should be copious production of KK-gravitons with mn=n/R<E ( m=1/R) - number of KK-states with m<E. Large NKK(E~MPl) compensates small 1/m. Pl 2, so ~ e/m. 6
2. Progress of phenomenological approach 3) ADD type models (or low energetic gravity). Another (negative and positive) consequences of ADD model: - Problem of overproduction of KK-gravitons in the early Universe. At T>>1/R KK-gravitons are produced with the rate Agreement with BBN and (modern) requires Conclusion is not changed in principle, if KK-gravitons are decayed before BBN. Low TR (~Me. V Ge. V), as obtained for MPl~1 Te. V, forces to muse anew upon the questions of baryosynthesis, inflation, dark matter origin in the early Universe. MPl>>1 Te. V (>10 30 Te. V) is preferable. - Constraint from SN 1987: agreement with an observed neutrino signal requires Generally it agrees with constrains from cosmology. 7
2. Progress of phenomenological approach 3) ADD type models (or low energetic gravity). Another (negative and positive) consequences of ADD model: + Solution of small masses of known neutrinos due to sterile neutrino with KK-states and mixed with ordinary ones. It can be provided, as well as for a bulk Plank mass, by large extra dimensions. * All possible physics of Grand Unification should take place at E MPl. In this case gauge constants should run following another law: a power-like law can be suggested (logarithmic law changes onto power-like starting from some until MPl). - As a consequence of low energetic GUT physics, a problem of fast proton decay appears. 8
2. Progress of phenomenological approach 3) RS type models (or low energetic gravity). RS – Randall, Sundrum There attempts to realize idea of solving hierarchy problem due to extra dimensions taking properly into account effect of gravity in a bulk space. In such configuration 4 d gravity constant on the brane at z=zc (with negative tension, RS-1) turns out to be reduced exponentially as compared to a bulk (5 d) gravity constant. k – curvature of the bulk space, can be ~MPl. Note, 5 d gravity constant has dimension here MPl-3. Lightest KK-gravitons has m~k (from point of view our brane) and interaction strength. There are different variations of such kind model: model with our world on the z=0 brane (RS-2: in this case there is no exponential suppression of our 4 d gravity constant with respect to 5 d one, but electroweak symmetry breaking can be connected with the second brane (z=zc) and in this manner relative exponential suppression can be reached), model with 3 branes, with intersecting branes. 9
3. Progress of fundamental theoretic approach 10
4. Birth of brane world A birth of brane(s) filled with matter and an empty interior bulk is a problem. 11
- Slides: 11